S hape Matching and Classification Using Height Functions

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S hape Matching and Classification Using Height Functions

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S hape Matching and Classification Using Height Functions

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Shape Matching and Classification Using Height Functions

Xide Xia

ENGN 2560

Advisor: Prof. Kimia

Project Initial Presentation

object recognition, character recognition, medical image and protein analysis …

- Geometric Transformations (translation, rotation, scaling, etc.)
- Nonlinear Deformations (noise, articulation and occlusion)

- 1) Shape descriptor with height functions
- 2) Similarity measure using the height descriptor

- A sequence of equidistant sample points X:
X={Xi} , i=1,2,….,N

- Tangent line Li:
its direction is always starting from Xi-1 to Xi+1

- Height value Hi:
the symboled distance between the jth (j = 1,. . . ,N) sample point Xj and the tangent line Li is defined as a height value hi,j.

(the height value of the jth sample point Xj according to the reference axis Li of the point Xi)

- the direction of the reference axis Li
- the location of the sample point Xi on the shape contour X.

- Smoothed height values:

F is an M *N matrix with column i being the shape descriptor Fi of the sample point Xi.

- Local nomalization:

Consequently, the value of each entry in the matrix F after normalization is in the interval [-1, 1].

In shape recognition, we usually compute a shape similarity or dissimilarity (distance) to find the optimal correspondence of contour points.

Dynamic Programming (DP) algorithm to find the correspondence

The shape dissimilarity: the sum of the distances of the corresponding points.

- The cost (distance) of matching p and q:
- Weight coefficient
- Dissimilarity between the two shapes:

Given two shapes X and Y. With DP we compute an optimal correspondence x to y that the is minimal.

Humans are generally more sensitive to contour deformations when the complexity of the contour is lower!

- Shape complexity:

where std denotes the standard deviation.

- The dissimilarity or distance between two shapes X, Y normalized by their shape complexity values:

where the factor is used to avoid divide-by-zero.

- A sequence of equidistant sample points X
- Tangent line Li
- Height value Hi
- Smoothed height values
- Local nomalization

Similarity measure using the height descriptor:

- The cost (distance) of matching p and q
- Weight coefficient
- Dissimilarity between the two shapes
- Shape complexity
- Dissimilarity normalized by complexity values

- 1st week: Learn the algorithm well
- 2nd ~3th week: Write up the codes of the shape descriptor part
- 4th ~5th week: Write up the codes of the matching part
- 6th~7th week: Debug and Test in different datasets, Make Comparison with other shape matching algorithm (Shock Graphs)
- 8th week: Make conclusion, Prepare for the final presentation

Thank you